But the decision, which came with little warning and reversed a more than century-old stance of determining gender based on birth certificates, further alienated many religious conservatives who were longtime advocates of the program.

“Now we see once again that the Boy Scouts really is committed to a gender-theory culture war that evangelical Christians and many other Americans just can’t accept,” said Russell Moore, the president of the Ethics & Religious Liberty Commission, the public policy arm of the Southern Baptist Convention.

Mr. Moore, a former scout, said Southern Baptist churches and others had been dismayed by Boy Scout policies for several years, as the Scouts moved first to allow openly gay youth members, and then openly gay adult leaders. Though several Southern Baptist congregations have stopped sponsoring Scout troops, Mr. Moore said others had held out hope that the organization would return to a more conservative worldview.

“I think, for some, this will be the final sign that it’s time to go,” Mr. Moore said.

Whether the new rules would lead to an influx of transgender scouts seemed uncertain. Besides one highly publicized case of a transgender boy being excluded from a New Jersey Scouting unit, there had been limited attention on the issue before this week. Boy Scouts officials declined to be interviewed, and would not comment on how many youths the decision might affect.

In a statement, a spokeswoman for the Boy Scouts said it was “no longer sufficient” to rely on a birth certificate to determine gender. “The B.S.A. is committed to identifying program options that will help us truly serve the whole family,” said the spokeswoman, Effie Delimarkos, adding that those efforts would remain “true to our core values, outlined in the Scout Oath and Law.”

For many years, the Boy Scouts have found themselves facing conflicting forces on issues of sexuality and inclusion. The Scouts contended with a pattern of declining membership, canceled corporate donations and public criticism over the group’s restrictions on gay youths before easing those rules in 2013. And the move this week to allow transgender youths was hailed by some as a positive, overdue step toward equality.

“No one should be denied the opportunity to participate in any Boy Scout troop because of their gender identity or expression,” Jonathan A. Greenblatt, the chief executive of the Anti-Defamation League, said in a statement.

But many Scout units are sponsored by conservative religious denominations that have opposed the changes, saying the organization has betrayed its values by loosening membership rules.

Tami Fitzgerald, the executive director of the North Carolina Values Coalition, said the transgender decision indicated that the Scouts “have diverged greatly from their founding principles.” Ms. Fitzgerald, who said her brother was an Eagle Scout, said the Values Coalition was now encouraging families to consider alternatives to the Boy Scouts.

Such conservative alternatives already exist. After the decision to allow gay members, John Stemberger, a former scoutmaster, pulled his sons out of the Boy Scouts and helped start a new program called Trail Life USA. Mr. Stemberger said Trail Life, which he described as a “distinctly Christian scouting organization,” was active in all but a few states with nearly 30,000 members, a tiny fraction of the roughly 2.3 million youths enrolled in Boy Scout programs.

Mr. Stemberger said he expected that the decision on transgender youths might prompt more families to enroll their sons in Trail Life. He said that the Boy Scouts’ transgender policy seemed inevitable given the change on gay membership, but that he was surprised by how quickly it came about.

“They are basically doing what gay activists want them to do because they lack the courage to defend their own tradition and their own Scout Oath and their own Scout Law,” Mr. Stemberger said.

Despite disenchantment from many on the right, the Boy Scouts have reported less pronounced membership declines in recent years. The Roman Catholic and Mormon churches, which collectively sponsor a large percentage of Scout units, have not left in overwhelming numbers, as some feared, and campouts, service projects and pinewood derbies have continued.

Whether allowing transgender boys to join will lead to significant departures remains unclear. Representatives of the United States Conference of Catholic Bishops and the Lutheran Church-Missouri Synod did not respond to requests for comment about the policy. The Mormon Church said in a statement that its leaders were studying the announcement.

But in some places, reaction was pointed and critical. A statement from the Catholic Archdiocese of St. Louis referred to transgender boys as “girls struggling with gender dysphoria,” said Boy Scout policies were “becoming increasingly incompatible with our Catholic values” and expressed hope that the Scouts would “recognize their error.”